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2021 | OriginalPaper | Buchkapitel

36. Unsteady Elastic–Diffusion Vibrations of a Simply Supported Euler–Bernoulli Beam Under the Distributed Transverse Load

verfasst von : Andrei V. Zemskov, Anatoly S. Okonechnikov, Dmitry V. Tarlakovskii

Erschienen in: Multiscale Solid Mechanics

Verlag: Springer International Publishing

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Abstract

The unsteady vibrations problem of a simply supported Euler–Bernoulli beam under the distributed transverse load is considered. For the mathematical problem formulation, we use the system of a beam deflections equations with inner diffusion processes. The system is obtained using the d’Alembert variational principle from a generalized elastic–diffusion problem with the nonzero diffusion fluxes relaxation. To solve the system, the Green’s function method is used. To find the Green’s functions, the Laplace integral transform and Fourier series expansion are used. The Laplace transform inversion is done using residues and operational calculus tables. Calculation examples are considered for a rectangular dural beam. The beam deflections and components concentration increments are calculated in the alloy under distributed transverse load. The influence of mass transfer and diffusion flows relaxation on the displacement field inside the beam is analyzed.

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Titel: Unsteady Elastic–Diffusion Vibrations of a Simply Supported Euler–Bernoulli Beam Under the Distributed Transverse Load
verfasst von: Andrei V. Zemskov
Anatoly S. Okonechnikov
Dmitry V. Tarlakovskii
Verlag: Springer International Publishing
Buch: Multiscale Solid Mechanics
Print ISBN: 978-3-030-54927-5

Electronic ISBN: 978-3-030-54928-2

Copyright-Jahr: 2021
DOI: https://doi.org/10.1007/978-3-030-54928-2_36

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